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The Penetration Equation
Technical details of the penetration equation are summarized below. For further discussion see R. E. Park, "Prospects for Cable in the 100 Largest Television Markets."
) = -8.159 + 3.098 log XN + 0.290 log XD
+0.212 log XI + 0.298 log Xe 0.540 log XF
= number of B-contour off-air OHF signals of type i
Vi = number of B-contour off-air VHF signals of type i
Pen= penetration = subscribers/households passed by cable
In order to use Park's estimated equation to predict penetration for the typical systems investigated in this report, representative values must be assigned to the variables of the equation. The following values are employed in all of the simulations:
P = $62.40, corresponding to the $5 per month plus $1
per month for 20% of subscribers as a charge for
C = 50%. The effect of varying color set penetration
is not estimated with sufficient precision to incorporate variations in color set ownership across different types of markets.
u = 80%
if o local network UHF signals
F = 0. Foreign stations are not included among the
signals carried by study systems.
In simulating cable systems for this study, we consider systems located in the central area of a television market, where off-the-air signal quality is generally high, and outlying areas of the same market, where quality is diminished. In the penetration equation the distance variable d is a measure of the reduction in quality. A d value of 0 corresponds to a viewer in the center of the market, while a value of 1 represents a viewer at the B-contour of the off-the-air signal.
For the systems in this study we have used the following values:
In middle markets:
d = 0 for local stations
In edge markets:
d = 0.5 for local stations
Tables 9 and 10, "Ten Percent Most Favorable Penetration conditions," are calculated using 133% of the penetration implied by Park's equation above. This corresponds approximately to the penetration value at the upper 10% confidence limit.
20-344 0.73 - 31
Households, Population and Density in Dayton, Ohio (Market No. 41)
Johnson, L. L., "Cable Communications in the Dayton Miami Valley: Basic Report." Table A2